We present a novel variational quantum framework for linear partial differential equation (PDE) constrained optimization problems. Such problems arise in many scientific and engineering domains. For instance, in aerodynamics, the PDE constraints are the conservation laws such as momentum, mass and energy balance, the design variables are vehicle shape parameters and material properties, and the objective could be to minimize the effect of transient heat loads on the vehicle or to maximize the lift-to-drag ratio. The proposed framework utilizes the variational quantum linear solver (VQLS) algorithm and a black box optimizer as its two main building blocks. VQLS is used to solve the linear system, arising from the discretization of the PDE constraints for given design parameters, and evaluate the design cost/objective function. The black box optimizer is used to select next set of parameter values based on this evaluated cost, leading to nested bi-level optimization structure within a hybrid classical-quantum setting. We present detailed computational error and complexity analysis to highlight the potential advantages of our proposed framework over classical techniques. We implement our framework using the PennyLane library, apply it to a heat transfer optimization problem, and present simulation results using Bayesian optimization as the black box optimizer. We also demonstrate that by using an alternative tensor product decomposition which better exploits the sparsity and structure of linear systems arising from PDE discretizations, one can substantially overcome the key computational bottleneck in VQLS arising from commonly employed Pauli basis for the linear combination of unitary (LCU) decomposition step within VQLS.

Recent advances in biological technologies, such as multi-way chromosome conformation capture (3C), require development of methods for analysis of multi-way interactions. Hypergraphs are mathematically tractable objects that can be utilized to precisely represent and analyze multi-way interactions. Here we present the Hypergraph Analysis Toolbox (HAT), a software package for visualization and analysis of multi-way interactions in complex systems.

With the advent of modern expert systems driven by deep learning that supplement human experts (e.g. radiologists, dermatologists, surveillance scanners), we analyze how and when do such expert systems enhance human performance in a fine-grained small target visual search task. We set up a 2 session factorial experimental design in which humans visually search for a target with and without a Deep Learning (DL) expert system. We evaluate human changes of target detection performance and eye-movements in the presence of the DL system. We find that performance improvements with the DL system (computed via a Faster R-CNN with a VGG16) interacts with observer's perceptual abilities (e.g., sensitivity). The main results include: 1) The DL system reduces the False Alarm rate per Image on average across observer groups of both high/low sensitivity; 2) Only human observers with high sensitivity perform better than the DL system, while the low sensitivity group does not surpass individual DL system performance, even when aided with the DL system itself; 3) Increases in number of trials and decrease in viewing time were mainly driven by the DL system only for the low sensitivity group. 4) The DL system aids the human observer to fixate at a target by the 3rd fixation. These results provide insights of the benefits and limitations of deep learning systems that are collaborative or competitive with humans.

The expansion of monitoring systems for power grids from the traditional transmission lines to include the distribution grid - closer to the end-user - is largely due to the advance in electrical monitoring devices and their increasing affordability. This paradigm-shift benefits from new algorithms that can be implemented at the grid edge (as opposed to the transmission grid) to detect anomalies faster, more efficiently, and in real-time. Micro-PMUs (μ-PMUs) are phasor measurement units that can be placed on the distribution lines to provide real-time data about the state of the grid and can detect fast transients. In this paper, we use data from (μ-PMUs to engineer physics-based features for a novel anomaly detection algorithm that detects anomalies based on the transient properties of the power grid. This allows for a more capable, agile, and reliable anomaly scoring system that can learn normal behavior patterns and detect anomalous behavior efficiently. We show that by combining the classical data-based approaches with physics-based features in the anomaly detection algorithm, the machine learning algorithm proposed is capable of detecting different classes of anomalies (such as edge devices on-off attacks, single line-to-ground (SLG) faults, etc.). Simulation results on IEEE 34-node test feeder show that we can achieve better detection performance than traditional techniques for a broader class of anomalies.

This paper outlines the development and testing of a novel, feedback-enabled attention allocation aid (AAAD), which uses real-time physiological data to improve human performance in a realistic sequential visual search task. Indeed, by optimizing over search duration, the aid improves efficiency, while preserving decision accuracy, as the operator identifies and classifies targets within simulated aerial imagery. Specifically, using experimental eye-tracking data and measurements about target detectability across the human visual field, we develop functional models of detection accuracy as a function of search time, number of eye movements, scan path, and image clutter. These models are then used by the AAAD in conjunction with real time eye position data to make probabilistic estimations of attained search accuracy and to recommend that the observer either move on to the next image or continue exploring the present image. An experimental evaluation in a scenario motivated from human supervisory control in surveillance missions confirms the benefits of the AAAD.

Simultaneous localization and mapping (SLAM) algorithms allow a single robot to reduce the effects of drifting sensor biases while exploring unknown, GPS-denied environments. To reduce exploration time, a team of robots can build smaller maps in parallel and perform map fusion. Most map fusion techniques require a known relative transformation between coordinate frames. Other techniques rely on inter-robot detections to estimate an initial transformation. However, large environments with sparse robot coverage may necessitate alternative techniques when robots are in communication, but not, sensor range. In this paper, we address the map fusion problem with unknown relative transformations between robot pairs. We use the probabilistic hypothesis density (PHD) SLAM algorithm to track features within a static, simulated environment and propose two techniques for distributed map matching: a RANSAC based congruent triangle matching algorithm and an earth mover's distance (EMD) based assignment algorithm.

In this paper we develop a Bayesian nonparametric Inverse Reinforcement Learning technique for switched Markov Decision Processes (MDP). Similar to switched linear dynamical systems, switched MDP (sMDP) can be used to represent complex behaviors composed of temporal transitions between simpler behaviors each represented by a standard MDP. We use sticky Hierarchical Dirichlet Process as a nonparametric prior on the sMDP model space, and describe a Markov Chain Monte Carlo method to efficiently learn the posterior given the behavior data. We demonstrate the effectiveness of sMDP models for learning, prediction and classification of complex agent behaviors in a simulated surveillance scenario.

We propose a hierarchical planning framework for mission planning and execution in uncertain and dynamic environments. We consider missions that involve motion planning in large, cluttered environments, trading off mission objectives while satisfying logical/spatial/temporal constraints. Our framework enables the decomposition of the planning problem across different layers, leveraging the difference in spatial and temporal scales of the mission objectives. We show that this framework facilitates contingency management under unanticipated events. Interaction between the various layers requires consistent model abstractions and common message semantics. To satisfy these requirements, we adopt a generic knowledge-based architecture that is independent from a specific application domain. We show a specific instance of our framework using a Constrained Markov Decision Process (CMDP) planner at the higher level and a Multi-Objective Probabilistic Roadmap (MO-PRM) planner at the lower level. The resulting planning system is tested in a realistic scenario where an agent is tasked with a mission in a large urban threat rich environment under dynamic uncertain conditions. The mission specification includes a Linear Temporal Logic (LTL) formula that defines the desired behaviors, a list of metrics to be optimized and a list of constraints on time, resources and probability of mission success.

There has recently been a significant amount of activity in developing supervisory control algorithms for multiple unmanned aerial vehicle operation by a single operator. While previous work has demonstrated the favorable impacts that arise in the introduction of increasingly sophisticated autonomy algorithms, little work has performed an explicit comparison of different types of multiple unmanned vehicle control architectures on operator performance and workload. This paper compares a vehicle-based paradigm (where a single operator individually assigns tasks to unmanned assets) to a task-based paradigm (where the operator generates a task list, which is then given to the group of vehicles that determine how to best divide the tasks among themselves.) The results demonstrate significant advantages in using a task-based paradigm for both overall performance and robustness to increased workload. This effort also demonstrated that while previous video gaming experience mattered for performance, the degree of experience that demonstrated benefit was minimal. Further work should focus on designing a flexible automated system that allows operators to focus on a primary goal, but also facilitate lower level control when needed without degradation in performance.

In this paper, we propose a hierarchical mission planner where the state of the world and of the mission are abstracted into corresponding states of a Markov Decision Process (MDP). Transitions in the MDP represent abstract motion actions that are planned by a lower level probabilistic planner. The cost structure of the MDP is multi-dimensional: each state-action pair is annotated with a vector of metrics such as time and resource requirements. A mission specification is divided into three parts: a temporal logic formula defined over state propositions, the choice of the primary cost, and constraints on the remaining secondary costs. The planning problem is formulated as finding the optimal policy of a Constrained Markov Decision Process with above mission specification. The resulting planning system is tested in a mission where an agent is tasked with a complex mission in a urban hostile environment.

We present an efficient planning algorithm for allocation and scheduling of spatially distributed tasks to multiple heterogenous resources (e.g. mobile sensors, robots) in presence of ordering constraints on task execution and environmental uncertainties. We use Process Algebra (PA) for capturing such constraints. Building on probabilistic timed PA semantics, we define a planning system in form of a transition system, capturing ordering and resource constraints, occurrence of uncontrollable events, task priorities and preemption, and task allocation/scheduling objectives represented as a cost function. We develop an anytime branch and bound algorithm to efficiently search this transition system, and compute optimal strategies which prescribe task allocation and schedules in response to all possible outcomes of uncontrollable events. Several examples are presented and results from numerical simulation of a vehicle routing problem are discussed.

We present a multiscale adaptive search algorithm for efficiently searching an unknown number of stationary targets using a team of multiple mobile sensors. We first derive a Spectral Multiscale Coverage (SMC) control law for a Dubins vehicle model. Given a search prior, the SMC control leads to uniform coverage dynamics for the mobile sensors such that the amount of time spent observing a region is proportional to finding a target in it. In order to make the search robust to sensor uncertainties and Automatic Target Detection algorithm errors (i.e. false alarm, missed detections), we combine the SMC control with decision and estimation theoretic techniques. As new targets are discovered we use the Sequential Ratio Probability Test and Recursive Least Squares estimation to quantify the current uncertainty in target detection and location, respectively. This uncertainty is used to update the search prior so as to balance exploitation (reduce uncertainty in state of already discovered potential targets) and exploration (discover new targets). We demonstrate this adaptive search methodology in a high fidelity simulation environment and show an improved performance over lawnmower type search.

For the universal hypothesis testing problem, where the goal is to decide between the known null hypothesis distribution and some other unknown distribution, Hoeffding proposed a universal test in the nineteen sixties. Hoeffding's universal test statistic can be written in terms of Kullback-Leibler (K-L) divergence between the empirical distribution of the observations and the null hypothesis distribution. In this paper a modification of Hoeffding's test is considered based on a relaxation of the K-L divergence, referred to as the mismatched divergence. The resulting mismatched test is shown to be a generalized likelihood-ratio test (GLRT) for the case where the alternate distribution lies in a parametric family of distributions characterized by a finite-dimensional parameter, i.e., it is a solution to the corresponding composite hypothesis testing problem. For certain choices of the alternate distribution, it is shown that both the Hoeffding test and the mismatched test have the same asymptotic performance in terms of error exponents. A consequence of this result is that the GLRT is optimal in differentiating a particular distribution from others in an exponential family. It is also shown that the mismatched test has a significant advantage over the Hoeffding test in terms of finite sample size performance for applications involving large alphabet distributions. This advantage is due to the difference in the asymptotic variances of the two test statistics under the null hypothesis.

The support vector machine (SVM) has emerged as one of the most popular approaches to classification and supervised learning. It is a flexible approach for solving the problems posed in these areas, but the approach is not easily adapted to noisy data in which absolute discrimination is not possible. We address this issue in this paper by returning to the statistical setting. The main contribution is the introduction of a statistical support vector machine (SSVM) that captures all of the desirable features of the SVM, along with desirable statistical features of the classical likelihood ratio test. In particular, we establish the following: (i) The SSVM can be designed so that it forms a continuous function of the data, yet also approximates the potentially discontinuous log likelihood ratio test. (ii) Extension to universal detection is developed, in which only one hypothesis is labeled (a semi-supervised learning problem). (iii) The SSVM generalizes the robust hypothesis testing problem based on a moment class. Motivation for the approach and analysis are each based on ideas from information theory. A detailed performance analysis is provided in the special case of i.i.d. observations. This research was partially supported by NSF under grant CCF 07-29031, by UTRC, Motorola, and by the DARPA ITMANET program. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF, UTRC, Motorola, or DARPA.